Your (Guy Delamarter's) complaint about MMa notation is exactly ontarget. (See below.) I don't have a solution but you might want to check outScientific Word/Workplace at for commercialsoftware which allows accessing MMa within a word processing/TeXenviornment. It has its own drawbacks as it provides for only a limitedaccess to MMa. In particular, you can't access your own functions, but itdoes provide for subscripts in the standard way. It's designed for doingpublishing, not mathematics.

In fact, your problem is an instance of a very much larger problem,and one which is the harbinger (hoefully) of a future system designed aroundthe concept that the notation/language used by mathematics/mathematicians isof first and central importance, and must take precedence over program(ming)artifact.

In short, you (Guy), are expecting an (interactive) programminglanguage designed by (primarily) programmers (not the mathematical content,though, presumably) to be similar to standard mathematical notation.However, the fact is, neither computational mathematics nor "very standard,accepted sort of notation" are up to it.

I have also used Macsyma since about 1974 at MIT and believe that,while MMa, Macsyma, Maple, ISETL, Prolog, etc., are major advances incomputational power/convienence (I use/have used all together with TeX andSci Workplace), for the most part, the "user languages" they provide arevery poorly designed. All are kludges making no distinction betweenprogramming artifact, logically sound mathematical semantics, issues ofrepresentation etc., with far too many redundant and overlapping functionsto learn, as opposed to a well thought out core of operations and datastructures. This becomes very evident when one attempts to move intonon-numeric mathematics, e. g., combinatorics, computational geometry etc.,etc.

However, mathematicians must also realize thatalgorithmic/representational oriented mathematics requires the introductionof a number of new concepts, as what you describe below as "very standard,accepted sort of notation" does not in fact exist, or at best isinsufficient for the modern job required.

In particular, the concepts of Church's lambda calculus, (andCurry's combinatorial logic), and Lisp, e. g., the idea, among others, thata function can control the evaluation of its arguments/domain (specialfunctions in Common Lisp, another kludge, in which the simplicity of theoriginal Lisp got lost) is central to the semantics of the new computationalmathematics and must be understood and incorporated into any implementationof it. (BTW, Slagle's Symbolic Automatic INTegrator (SAINT, 1961) and JoelMoses's Macsyma (1967) were both written in Lisp and precisely because theyprovided both a theoretical basis as well as a convenient one.)

A very simple example of the two approaches (computational versus"standard math") is the "quote" function of Lisp/MMa and the concept of the"identity" function in mathematics, and must somehow be combined so as to beviewed as the same sematic operation.

My personal belief is that something on the order of 25-50"notational schemas" of a very general, complimentary and nonredundantnature, complimented with the appropriate "data structures", will sufficefor providing a common base for further extensions into specialized areas ofmathematics incorporating add on packages etc.

The point of this "diatribe" is that the community is in a state oftransition. The current sate of affairs in which the mathematics communityis forced to put up with two parallel notations within which to expressitself cannot long endure. The concepts/notation schemas are there, but itwill take (a) new beginning(s) to build a "computer algebra" system whichsimultaneously provides the mathematical community an acceptable notationfor communication with other humans as well as provideing a notation forrepresentation/algorithmic specification.

I do not have all the answers, or for that matter, any of them, butI would like to see some organized attempt at understanding these long term(twenty five years) very important issues, Guy having brought a very goodinstance to our attention. The "efficiency" at which the community doesfuture mathematics is at stake.

Sorry to get so long winded and hope this is not too much out ofplace for this forum.

Don J. Orserdjorser@intrepid.net

>My department has finally purchased and installed Mathematica 3.0 and>I was looking forward to using variable names that LOOKED like the>variables I use in and read from technical documents. However, it>appears that Mathematica assumes that subscripts are array indicies.>I would gladly give up the ability to use subscripts as array>addressing and use square brackets instead, if I could then use>subscripts to denote unique names. For example, I would like it so>that (using TeX notation, where _ denotes subscript) R_{sub} is a>totally independent variable from R_{x}. As it stands now, the former>accesses the sub'th element of R and the latter accesses the x'th>element of R - and assumes R is some sort of array. In some cases>this is okay, in others it isn't. One case where it isn't is when I>want to define R_{sub} in terms of R_{x}. I obtain recusrsion in that>case. Another case is where I want to apply Clear to R_{x}, but not>R_{sub}.>>Since what I am asking for is the ability to write in a very standard,>accepted sort of notation, I would hope that 3.0 has a way of obtaining it.>>Thanks,>Guy Delamarter>>-- >==============================================================================>Guy Delamarter <delamart@callisto.pas.rochester.edu>>******************************************************************************